hello
how do we convert a number into fraction for example :
1.75 = 7/4
0.111... = 1/9
.001=1/1000
how to solve that? please i need help!
Thanks
You can convert a fraction into a decimal by dividing the top number (numerator) by the bottom number (denominator). Here's an example:
1/2 = 1 ÷ 2 = 0.5 (= 50%)
Try it with the others.
Here are some good math websites to help with fractions, decimals, and many other math topics:
http://www.aaamath.com/
http://www.mathisfun.com/ >> http://www.mathsisfun.com/numbers/index.html
http://mathforum.org/dr.math/ >> http://mathforum.org/library/drmath/drmath.elem.html
And here's a good website to use when you want to check your work:
http://www51.wolframalpha.com/
It looks like you already know how. In the first case, just convert the decimal to a mixed number by writing out the fraction part as tenths or hundredths, etc, and reduce the fraction to lowest terms.
In the last case, do the same thing.
The second case, a repeating decimal, is a bit trickier. You have to multiply the number by a power of 10 that causes the repeating decimal to shift and realign with the same numbers above and below. The do a subtraction that leaves you with just integers. For example:
x = 0.142857142857...
1,000,000x = 142857.142857...
999,999x = 142857
x = 142857/999,999 = 1/7
Here is a short-cut algorithm to convert a repeating decimal to a fraction
e.g. 0.12345345345...
numerator:
skipping the decimal, write down all the digits to the end of the first repeat, from that, subtract all the digits that don't repeat
i.e. 12345-12 = 12333
for the denominator:
write down a 9 for each repeating digit, followed by a 0 for each non-repeating digit
i.e. 99900
so .12345345345... = 12333/99900
4111/33300
or for dwrls example of .142857142857..
= (142857 - 0)/999999 = 1/7
for .11111 = (1-0)9
= 1/9
Hello! I'd be happy to help you with converting numbers into fractions.
To convert a number into a fraction, you need to understand the decimal representation of the number you are trying to convert. I'll explain the process using the examples you provided.
1. To convert 1.75 into a fraction, first identify the place value of each digit after the decimal point. In this case, the 7 is in the tenths place and the 5 is in the hundredths place.
2. Next, write the number without the decimal point as the numerator and the place value as the denominator. In this case, the numerator will be 175 (1.75 without the decimal point) and the denominator will be 100 (because the number has two decimal places).
3. Simplify the fraction if possible. In this example, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 25. So the simplified fraction is 7/4.
To convert recurring decimals (decimal numbers with repeating patterns) into fractions, follow these steps:
1. Identify the repeating pattern. In the case of 0.111..., the digit 1 repeats infinitely.
2. Write an equation to represent the recurring decimal. Let x represent the recurring decimal: x = 0.111...
3. Multiply both sides of the equation by 10 to shift the decimal point: 10x = 1.111...
4. Subtract the original equation from the shifted equation: 10x - x = 1.111... - 0.111...
5. Simplify the equation: 9x = 1. (On the right side, the repeating pattern cancels out)
6. Solve for x by dividing both sides of the equation by 9: x = 1/9.
So, 0.111... is equal to 1/9.
For a number like 0.001, it can be written as 1/1000, where the denominator is determined by the number of zeros after the decimal point.
I hope this explanation helps you! Let me know if you have any further questions.